Self-determination theory (SDT) proposes to explain the relations between motivational states and human development. In education, a central tenet of the theory is that experiencing autonomous motivation in school activities (i.e., genuine pleasure and enjoyment) fosters optimal learning processes, whereas experiencing controlled motivation (i.e., pressure from social or instrumental incentives) undermines them. Although the theory is well established empirically, little is known about how these motivations combine in their effects on achievement at school (interactions), and whether their effects depend on the intensity of motivations (nonlinearities) or on the context of study (national differences). Applying cubic response surface analysis to the TIMSS 2019 dataset on mathematics (N = 152,825 8th grade students from 37 countries), as well as replication data (N = 169,269 8th grade students from TIMSS 2015, N = 270 college students from SDT data), this study uncovers the existence of various kinds of nonlinear-interactive motivational processes in achievement, three of which systematically account for cross-national differences. In substance, these findings demonstrate that predictions based on SDT are close to universally true (93% of students), although they may not generalize well to extreme states of autonomous or controlled motivation (nonlinear and interactive processes). Implications for research and interventions on motivational processes are discussed.